Transient analysis of layered composite plates accounting for transverse shear strains and von Karman strains

Abstract

The increasing use of laminated composites in moving structures such as aircraft has led to a need for an efficient and accurate procedure for performing transient bending analysis of laminated composite plates. Classical theory is inadequate because it neglects transverse shear deformation, rotatory inertia, and geometric nonlinearities.

In this thesis, a theory to account for transverse shear deformation and rotatory inertia is combined with the von Karman theory of geometric nonlinearities to develop the nonlinear governing equations of laminated composite plate bending. A finite element program is developed to solve these equations, using the Newmark direct integration technique to integrate the equations in time. Apparently, this constitutes the first transient finite-element analysis of laminated composite plate bending which accounts for transverse shear deformation, rotatory inertia, and geometric nonlinearities. The program accuracy is verified by comparison with results previously reported in the literature. Finally, results of a study of various material and plate geometry parameters are presented.

The results of the parametric study show that transverse shear deformation, rotatory inertia, and geometric nonlinearity may all have a profound effect on the predicted bending response. In addition, the effects of material orthotropy, plate aspect ratio, plate thickness, lamination scheme, and load magnitude are shown to be significant. Computational constants such as the Newmark coefficients, the time-step size, and the element mesh are also investigated, and appropriate observations are made on the computational aspects of the program.